Question

Figure 5 below shows a battery consisting of three cells. Their emfs and internal resistances are also shown.

Calculate:

1. Emf of the battery.
2. Internal resistance of the battery.

Answer 1

(a) Top branch of emf (E₁) = 2 V + 4 V

= 6 V

Bottom branch of emf (E₂) = 6 V

The parallel combination of both branches has the same EMF (6 V); the total EMF is simply the value of one branch.

`E_"total" = 6 V`

(b) Top Branch Resistance (r₁) = 1 Ω + 3 Ω

= 4 Ω

Bottom Branch Resistance (r₂) = 12 Ω

Parallel Resistance `r_"total"` of both branches is:

`1/(r_"total") = 1/4 + 1/12`

= `(3 + 1)/12`

= `4/12`

= `1/3`

∴ `r_"total" = 3  Ω`